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Conductors, Insulators, and Semiconductors

Source lecture(s): SC134 Lec1

Intuition

Materials respond to electric fields differently depending on how freely charges can move.

Formal Definition

Conductors have free charge carriers; insulators do not; semiconductors are intermediate and tunable.

Mathematical Formulation

Current density: \(\vec{J} = nq\vec{v}_d\) Resistivity: \(\rho = E/J\)

Derivation

Drude model treats conduction electrons as a gas; Ohm's law emerges from average drift under \(E\).

Worked Example

Copper: \(\sigma\approx 5.8\times10^7\,\text{S/m}\). Silicon: tunable from \(10^{-3}\) to \(10^4\,\text{S/m}\).

Common Mistakes

  • Confusing conductivity (\(\sigma\)) with resistivity (\(\rho\)).
  • Assuming superconductors have zero resistance only at room temperature.

Quiz

Q1. Which class has tunable conductivity?

Answer

Semiconductors.